Highest Waves of Permanent Type on the Surface of Deep Water

This is the authors' abstract. We don't add key points for this paper.

Resume.-Under the Levi-Civita's formulation th<' highest waves on thl' surface of deep water was calculated.For !! = 0 + i r we assume the form ! log(l -C) +:Ea,.C"; a's art> 12 in number.C is the unit cirde corresponding to water region, and 0(,1), :-(,1) on the circumfrrenn ( = e 1 a (-n < 11 s 1t) solve the problem.To obtain 0(11), r(,1) w, us..-an itC'ratin procedure:-, one cycle of it consisting of two stages: to get ,(,1) from 0(,1) through the surface condition and to get 0(11), the harmonic conjugate of r(11), Calculations were all numerical and almost con\"c:-rged aftc:-r 8 cyclc:-s.Obtained results fulfil the susface condition with %error.One refinement of approximation is proposc:-d and error is reduced to one third.